A383228 a(n) is the number of cases where both j and k (1 <= j < k <= n), are divisors of Sum_{i=j..k} i^i.

0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17

Offset

1,6

Links

Jean-Marc Rebert, Table of n, a(n) for n = 1..1000

Example

1 and 4 divide Sum_{i = 1..4} i^i = 288, and
1 and 17 divide Sum_{i = 1..17} i^i = 846136323944176515621, and
1 and 19 divide Sum_{i = 1..19} i^i = 2018612200059554303215024, and
2 and 9 divide Sum_{i = 2..9} i^i = 405071316, and
2 and 30 divide Sum_{i = 2..30} i^i = 208492413443704093346554910065262730566475780, and
3 and 6 divide Sum_{i = 3..6} i^i = 50064, and
5 and 15 divide Sum_{i = 5..15} i^i = 449317984130199540, and
14 and 42 divide Sum_{i = 14..42} i^i = 151474018115847331407847533862930150275321445330384244581082952733296, and
22 and 26 divide Sum_{i = 22..26} i^i = 6246292379849897330286605654999947328, so a(42) = 9.

Prog

(PARI) a(n) = sum(j=1, n, sum(k=j+1, n, my(s=sum(i=j, k, i^i)); !(s % j) && !(s % k))); \\ Michel Marcus, Apr 20 2025

Crossrefs

Cf. A000312, A001923, A128981.

Sequence in context: A070564 A072358 A074795 * A069577 A282426 A318781

Adjacent sequences: A383225 A383226 A383227 * A383229 A383230 A383231

Keyword

nonn

Author

Jean-Marc Rebert, Apr 20 2025

Extensions

More terms from Michel Marcus, Apr 20 2025

Status

approved